Queuing Theory for the Infirm

Although I now find it hard to justify, I can definitively assert that using those
little weekly pill holders that old folks get at the pharmacy is more efficient than
getting one pill out of each bottle every day.  How do I know this?

It was a Saturday morning, breakfast was over, and the coffee was downed (a lot
of it).  In the throws of a conversation about vitamin taking, my
wife alleged that using a weekly pill organizer would be faster than opening each
bottle on a daily basis, as I do with no less than 4 pills every morning.  She
was so steadfastly secure in her opinion that she stared me down in what I took to
be direct challenge.  After all, UPS created a company on the idea that a package
(in this case a pill) should be touched as few times as possible on it’s route to
delivery.

What next?  I got a weekly pill organizer, a stopwatch, 4 pill bottles, and some
paper with which to record my findings.  Trials were run in groups of 3 attempts
each, with one minute resets in between.  The bottles were scattered across my
kitchen table to better simulate finding them in the drawer each morning.  The
findings weren’t as drastically different as you might expect. 

Direct From the Bottle

For each of the three runs, I reloaded and scattered the pill bottles.  After
Elle hit “Go” on the stop watch, I opened and closed each pill bottle successively,
placing a single pill from each in a pile in front of me.  The timer was stopped
after the last bottle was recapped and discarded.

Run 1: 26 seconds

Run 2: 22 Seconds

Run 3: 27 Seconds

Average Time: 25s. X 7 days per week = 1:55 / week.

Filling Up the Weekly Pill Holder

The next question is simple.  Is it faster to load a single weekly pill holder
with 4 pills per day such that they can be easily ingested without processing each
pill bottle every morning.  For each run, I reloaded and scattered the bottles
on the table.  Each test run was processed with the most efficient technique
that my hands found for that run with each run differing a bit based on the situation. 
For instance, in run two I spilled the pills into my second hand and counted
out 7 pills after learning in run one that doing this on the table would
cost me time.

Run 1: 94 Seconds

Run 2: 94 Seconds (amazing, no?)

Run 3: 88 Seconds

Average Time: 1:32 / week to load the pill holder.

Conclusion

Upon first glance it may appear that UPS got it wrong.  That the pills were handled
one extra time using the pill holder leads us to believe that the duration will
be greater from bottle to ingestion because of the extra handling time.  Obviously
this isn’t the case and handling the pills one extra time by putting them into a central
organizer turns out to be more efficient after all.

In fact the efficiency we are gaining here is in handling the bottle fewer times,
not unlike applying organization to the UPS truck instead of the packages themselves. 
We can therefore conclude that efficiencies applied to containers will be visited
upon the contents of those containers.  I propose that the rate at which that
efficiency is realized can be represented as a “parental efficiency coefficient”,
representing the divisible container efficiency as a multiple of the number of
children divided by the amount of work applied to the parent.

It would appear that Elle was right.  I have no idea if my efficiency coefficient
is an already proven constant, but by golly it should be, and by someone who something
better to do on a Saturday morning.